The six game ordering associated with the fixation of dominating strategies [1]} (also named unbeatable in the literature [2]}, [3]}), such as defectors under the Prisoner's Dilemma [4]}, [5]}, were observed to hold monotonically decreasing functions, with one complete ordering and subsets of some of the remaining being comprehended in the conditions of Theorems 1 and 2. However, they were also shown to have a wide variety of other function shapes. Functions with one global minimum were observed under five out of the six orderings. Under three of these orderings, we observed monotonically increasing functions. Two of them additionally showed alternative functions keeping an initial increase but decreasing for larger population sizes, and also functions with two extremes when transitioning between those with a global minimum and the previous shape. On the other side, the fixation of dominated strategies, such as Cooperation under the same games, was proved or tested to systematically hold monotonically decreasing functions.
